Math

GeometryElementary Geometry for College Studentsa) Find a lower estimate of the area of the figure by counting whole squares within the figure. b) Find an upper estimate of the area of the figure by counting whole and partial squares within the figure. c) Use the average of the results in parts (a) and (b) to provide a better estimate of the area of the figure. d) Does intuition suggest that the area estimate of part (c) is the exact answer?BuyFind*arrow_forward*

6th Edition

Daniel C. Alexander + 1 other

Publisher: Cengage Learning

ISBN: 9781285195698

Chapter 8.1, Problem 55E

Textbook Problem

a) Find a lower estimate of the area of the figure by counting whole squares within the figure.

b) Find an upper estimate of the area of the figure by counting whole and partial squares within the figure.

c) Use the average of the results in parts (a) and (b) to provide a better estimate of the area of the figure.

d) Does intuition suggest that the area estimate of part (c) is the exact answer?

Elementary Geometry for College Students

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Ch. 8.1 - Suppose that two triangles have equal areas. Are...Ch. 8.1 - The area of the square is 12, and the area of the...Ch. 8.1 - Consider the information in Exercise 2, but...Ch. 8.1 - If MNPQ is a rhombus, which formula from this...Ch. 8.1 - In rhombus MNPQ, how does the length of the...Ch. 8.1 - When the diagonals of rhombus MNPQ are drawn, how...Ch. 8.1 - ABC is an obtuse triangle with obtuse angle A. DEF...Ch. 8.1 - Are ABC and DEF congruent? Exercises 7, 8Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...

Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 19 to 22, find the area of the shaded...Ch. 8.1 - In Exercises 19 to 22, find the area of the shaded...Ch. 8.1 - In Exercises 19 to 22, find the area of the shaded...Ch. 8.1 - In Exercises 19 to 22, find the area of the shaded...Ch. 8.1 - A triangular corner of a store has been roped off...Ch. 8.1 - Carpeting is to be purchased for the family room...Ch. 8.1 - The exterior wall the gabled end of the house...Ch. 8.1 - The roof of the house shown needs to be...Ch. 8.1 - A beach tent is designed so that one side is open....Ch. 8.1 - Gary and Carolyn plan to build the deck shown. a...Ch. 8.1 - A square yard is a square with sides 1 yard in...Ch. 8.1 - The following problem is based on this theorem: A...Ch. 8.1 - For Exercise 31 and 32, X is the midpoint of VT...Ch. 8.1 - For Exercise 31 and 32, X is the midpoint of VT...Ch. 8.1 - Given ABC with midpoints M, N and P of the sides,...Ch. 8.1 - In Exercises 34 to 36, provide paragraph proofs....Ch. 8.1 - In Exercises 34 to 36, provide paragraph proofs....Ch. 8.1 - In Exercises 34 to 36, provide paragraph proofs....Ch. 8.1 - Given: The area of right ABC not shown is 40in2....Ch. 8.1 - The lengths of the legs of a right triangle are...Ch. 8.1 - Given: ABC, whose sides are 13 in., 14 in., and 15...Ch. 8.1 - Given: ABC, whose sides are 10 cm, 17 cm, and 21...Ch. 8.1 - If the length of the base of a rectangle is...Ch. 8.1 - If the length of the base of a rectangle is...Ch. 8.1 - Given region RS, explain why ARSAR.Ch. 8.1 - Given region RST, explain why ARSTAR+AS+AT.Ch. 8.1 - The algebra method of FOIL multiplication is...Ch. 8.1 - Use the square configuration to complete the...Ch. 8.1 - In Exercises 47 to 50, use the fact that the area...Ch. 8.1 - In Exercises 47 to 50, use the fact that the area...Ch. 8.1 - In Exercises 47 to 50, use the fact that the area...Ch. 8.1 - In Exercises 47 to 50, use the fact that the area...Ch. 8.1 - The area of a rectangle is 48in2. Where x is the...Ch. 8.1 - The perimeter of the rectangle is 32 cm. Where x...Ch. 8.1 - Square DEFG is inscribed in right ABC, as shown....Ch. 8.1 - TV bisects STR of STR. ST=6 and TR=9. If the area...Ch. 8.1 - a Find a lower estimate of the area of the figure...Ch. 8.1 - a Find a lower estimate of the area of the figure...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 9 and 10, use Herons Formula. Find...Ch. 8.2 - In Exercises 9 and 10, use Herons Formula. Find...Ch. 8.2 - For Exercises 11 and 12, use Brahmaguptas Formula....Ch. 8.2 - For Exercises 11 and 12, use Brahmaguptas Formula....Ch. 8.2 - In Exercises 13 to 18, find the area of the given...Ch. 8.2 - In Exercises 13 to 18, find the area of the given...Ch. 8.2 - In Exercises 13 to 18, find the area of the given...Ch. 8.2 - In Exercises 13 to 18, find the area of the given...Ch. 8.2 - In Exercises 13 to 18, find the area of the given...Ch. 8.2 - In Exercises 13 to 18, find the area of the given...Ch. 8.2 - In a triangle of perimeter 76 in., the length of...Ch. 8.2 - In a triangle whose area is 72 in2, the base has a...Ch. 8.2 - A trapezoid has an area of 96 cm2. If the altitude...Ch. 8.2 - The numerical difference between the area of a...Ch. 8.2 - Find the ratio A1A2 of the areas of two similar...Ch. 8.2 - Find the ratio A1A2 of the areas of two similar...Ch. 8.2 - In Exercises 25 and 26, give a paragraph form of...Ch. 8.2 - In Exercises 25 and 26, give a paragraph form of...Ch. 8.2 - In Exercises 27 to 30, find the area of the figure...Ch. 8.2 - In Exercises 27 to 30, find the area of the figure...Ch. 8.2 - In Exercises 27 to 30, find the area of the figure...Ch. 8.2 - In Exercises 27 to 30, find the area of the figure...Ch. 8.2 - Mary Frances has a rectangular garden plot that...Ch. 8.2 - The perimeter of a right triangle is 12 m. If the...Ch. 8.2 - Farmer Watson wishes to fence a rectangular plot...Ch. 8.2 - The farmer in Exercise 33 has decided to take the...Ch. 8.2 - Find the area of the room whose floor plan is...Ch. 8.2 - Find the perimeter of the room in Exercise 35.Ch. 8.2 - Examine several rectangles, each with a perimeter...Ch. 8.2 - Examine several rectangles, each with an area of...Ch. 8.2 - Square RSTV is inscribed in square WXYZ, as shown....Ch. 8.2 - Square RSTV is inscribed in square WXYZ, as shown....Ch. 8.2 - For Exercises 41 and 42, the sides of square ABCD...Ch. 8.2 - For Exercises 41 and 42, the sides of square ABCD...Ch. 8.2 - Although not all kites are cyclic, one with sides...Ch. 8.2 - Although not all trapezoids are cyclic, one with...Ch. 8.2 - For Exercises 45 and 46, use this information: Let...Ch. 8.2 - For Exercises 45 and 46, use this information: Let...Ch. 8.2 - Prove that the area of a trapezoid whose altitude...Ch. 8.2 - For Exercises 48 and 49, use the formula found in...Ch. 8.2 - For Exercises 48 and 49, use the formula found in...Ch. 8.2 - Prove that the area of a square whose diagonal has...Ch. 8.2 - For Exercises 51 and 52, use the formula found in...Ch. 8.2 - For Exercises 51 and 52, use the formula found in...Ch. 8.2 - The shaded region is that of a trapezoid....Ch. 8.2 - Trapezoid ABCD not shown is inscribed in O so that...Ch. 8.2 - Each side of square RSTV has length 8. Point W...Ch. 8.2 - For the cyclic quadrilateral MNPQ, the sides have...Ch. 8.3 - Find the area of a square with a sides of length...Ch. 8.3 - Find the area of a square with a a perimeter of...Ch. 8.3 - Find the area of an equilateral triangle with a...Ch. 8.3 - Find the area of an equiangular triangle with a a...Ch. 8.3 - In a regular polygon, each central angle measures...Ch. 8.3 - In a regular polygon, each interior angle measures...Ch. 8.3 - For a regular hexagon, the length of the apothem...Ch. 8.3 - For a regular hexagon, the length of the radius is...Ch. 8.3 - In a particular type of regular polygon, the...Ch. 8.3 - In a particular type of regular polygon, the...Ch. 8.3 - In one type of regular polygon, the measure of...Ch. 8.3 - If the area (A=12aP) and the perimeter of a...Ch. 8.3 - Find the area of a square with apothem a = 3.2 cm...Ch. 8.3 - Find the area of an equilateral triangle with...Ch. 8.3 - Find the area of an equilateral triangle with...Ch. 8.3 - Find the area of a square with apothem a = 8.2 ft...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - Find the ratio of the area of a square...Ch. 8.3 - Given regular hexagon ABCDEF with each side of the...Ch. 8.3 - Given a regular octagon RSTUVWXY with each side of...Ch. 8.3 - Regular octagon ABCDEFGH is inscribed in a circle...Ch. 8.3 - Given regular pentagon RSTVQ and equilateral...Ch. 8.3 - Consider regular pentagon RSTVQ not shown. Given...Ch. 8.3 - Consider a regular hexagon ABCDEF not shown. By...Ch. 8.3 - The length of each side of a regular hexagon...Ch. 8.4 - Find the exact circumference and area of a circle...Ch. 8.4 - Find the exact circumference and area of a circle...Ch. 8.4 - Find the approximate circumference and area of a...Ch. 8.4 - Find the approximate circumference and area of a...Ch. 8.4 - Find the exact lengths of the radius and the...Ch. 8.4 - Find the approximate lengths of the radius and the...Ch. 8.4 - Find the exact lengths of the radius and the...Ch. 8.4 - Find the exact length of the radius and the exact...Ch. 8.4 - Find exactly lAB, where AB refers to the minor arc...Ch. 8.4 - Find exactly lCD for the minor arc shown.Ch. 8.4 - Use your calculator value of to find the...Ch. 8.4 - Use your calculator value of to find the...Ch. 8.4 - A metal circular disk whose area is 143 cm2 is...Ch. 8.4 - A circular lock washer whose outside circumference...Ch. 8.4 - The central angle corresponding to a circular...Ch. 8.4 - Use your calculator to find the approximate...Ch. 8.4 - A rectangle has a perimeter 16 in. What is the...Ch. 8.4 - A rectangle has an area of 36 in2. What is the...Ch. 8.4 - The legs of an isosceles triangle each measure 10...Ch. 8.4 - Two sides of a triangle measure 5 in and 7 in....Ch. 8.4 - Let N be any point on side BC of the right...Ch. 8.4 - What is the limit of mRTS if T lies in the...Ch. 8.4 - In exercises 23-26, find the exact areas of shaded...Ch. 8.4 - In exercises 23-26, find the exact areas of shaded...Ch. 8.4 - In exercises 23-26, find the exact areas of shaded...Ch. 8.4 - In exercises 23-26, find the exact areas of the...Ch. 8.4 - In Exercises 27 and 28, use your calculator value...Ch. 8.4 - In Exercises 27 and 28, use your calculator value...Ch. 8.4 - Assuming that a 90 arc has an exact length 4 in.,...Ch. 8.4 - The ratio of the circumferences of two circles is...Ch. 8.4 - Given concentric circles with radii of lengths R...Ch. 8.4 - Given a circle with diameter of length d, Explain...Ch. 8.4 - The radii of two concentric circles differ in...Ch. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - The diameter of a carousel merry-go-round is 30ft....Ch. 8.4 - A tabletop is semicircular when its three...Ch. 8.4 - Given that the length of each side of a rhombus is...Ch. 8.5 - Given O with radii OA- and OB- and chord AB-....Ch. 8.5 - Given O with radii OA- and OB- and chord AB-....Ch. 8.5 - In the semicircular region shaded DQ=6". a Find...Ch. 8.5 - For the semicircular region of Exercise 3, the...Ch. 8.5 - In the circle, the radius length is 10 in. and the...Ch. 8.5 - If the area of the circle is 360 in2, what is the...Ch. 8.5 - If the area of 1200 sector is 50 cm2, what is the...Ch. 8.5 - If the area of the 1200 sector is 40 cm2 and the...Ch. 8.5 - Suppose that a circle of radius r is inscribed in...Ch. 8.5 - Suppose a circle of radius r is inscribed in a...Ch. 8.5 - Find the perimeter of a segment of a circle whose...Ch. 8.5 - A sector with perimeter 30 in. has a bounding arc...Ch. 8.5 - A circle is inscribed in a triangle having sides...Ch. 8.5 - A circle is inscribed in a triangle having sides...Ch. 8.5 - A triangle with sides of lengths 3 in., 4 in., and...Ch. 8.5 - The approximate area of a triangle with sides of...Ch. 8.5 - Find the exact perimeter and area of the sector...Ch. 8.5 - Find the exact perimeter and area of the sector...Ch. 8.5 - Find the approximate perimeter of the sector...Ch. 8.5 - Find the approximate area of the sector shown....Ch. 8.5 - Find the exact perimeter and area of the segment...Ch. 8.5 - Find the exact perimeter and area of the segment...Ch. 8.5 - In Exercises 23 and 24, find the exact areas of...Ch. 8.5 - In Exercises 23 and 24, find the exact areas of...Ch. 8.5 - Assuming that the exact area of a sector...Ch. 8.5 - For concentric circles with radii of lengths 3 in....Ch. 8.5 - A circle can be inscribed in the trapezoid shown....Ch. 8.5 - A circle can be inscribed in an equilateral...Ch. 8.5 - In a circle whose radius has length 12 m, the...Ch. 8.5 - At the Pizza Dude restaurant, a 12-in. pizza costs...Ch. 8.5 - At the Pizza Dude restaurant, pizza is sold by the...Ch. 8.5 - Determine a formula for the area of the shaded...Ch. 8.5 - Determine a formula for the area of the shaded...Ch. 8.5 - Find a formula for the area of the shaded region,...Ch. 8.5 - A company logo on the side of a building shows an...Ch. 8.5 - In a right triangle with sides of lengths a, b and...Ch. 8.5 - In a triangle with sides of lengths a, b and c and...Ch. 8.5 - Use the results from Exercises 36 and 37 to find...Ch. 8.5 - Use the results from Exercises 36 and 37 to find...Ch. 8.5 - Three pipes, each of radius length 4 in., are...Ch. 8.5 - A windshield wiper rotates through a 1200 angle as...Ch. 8.5 - A goat is tethered to a barn by a 12-ft chain. If...Ch. 8.5 - An exit ramp from one freeway to another freeway...Ch. 8.5 - In ABC,mC=90 and mB=60. If AB=12 in., find the...Ch. 8.5 - A triangle has sides of lengths 6 cm, 8 cm and 10...Ch. 8.CR - For the Review Exercises, give an exact answer...Ch. 8.CR - For the Review Exercises, give an exact answer...Ch. 8.CR - For the Review Exercises, give an exact answer...Ch. 8.CR - In Review Exercises 4 to 5, drawABC , if...Ch. 8.CR - In Review Exercises 4 to 5, drawABC , if...Ch. 8.CR - Given: Trapezoid ABCD, with...Ch. 8.CR - Given: Trapezoid ABCD, with AB=6andBC=8,ABCD Find:...Ch. 8.CR - Find the area and the perimeter of a rhombus whose...Ch. 8.CR - Tom Morrow wants to buy some fertilizer for his...Ch. 8.CR - Alices mother wants to wallpaper two adjacent...Ch. 8.CR - Given: Isosceles trapezoid ABCD Equilateral FBC...Ch. 8.CR - Given: Kite ABCD withAB=10BC=17,andBD=16 Find:...Ch. 8.CR - One side of a rectangle is 2 cm longer than a...Ch. 8.CR - One side of a triangle is 10 cm longer than a...Ch. 8.CR - Find the area of ABD as shown.Ch. 8.CR - Find the area of an equilateral triangle if each...Ch. 8.CR - If AC is a diameter of O, find the area of the...Ch. 8.CR - For a regular pentagon, find the measure of each:...Ch. 8.CR - Find the area of a regular hexagon, each of whose...Ch. 8.CR - The area of an equilateral triangle is 1083in2. If...Ch. 8.CR - Find the area of a regular hexagon whose apothem...Ch. 8.CR - In a regular polygon, each central angle measures...Ch. 8.CR - Can a circle be circumscribed about each of the...Ch. 8.CR - Can a circle be inscribed in each of the following...Ch. 8.CR - The length of the radius of a circle inscribed in...Ch. 8.CR - The Turners want to install outdoor carpet around...Ch. 8.CR - Find the exact areas of the shaded regions in...Ch. 8.CR - Find the exact areas of the shaded regions in...Ch. 8.CR - Find the exact areas of the shaded regions in...Ch. 8.CR - Find the exact areas of the shaded regions in...Ch. 8.CR - Find the exact areas of the shaded regions in...Ch. 8.CR - The arc of a sector measures 40. Find the exact...Ch. 8.CR - The circumference of a circle is 66 ft. aFind the...Ch. 8.CR - A circle has an exact area of 27ft2. aWhat is the...Ch. 8.CR - An isosceles right triangle is inscribed in a...Ch. 8.CR - Given : Concentric circles with radii of lengths R...Ch. 8.CR - Prove that the area of a circle circumscribed...Ch. 8.CR - Prove that if semicircles are constructed on each...Ch. 8.CR - Jeff and Helen want to carpet their family room,...Ch. 8.CR - Sue and Daves semicircular driveway is to be...Ch. 8.CT - Complete each statement. a Given that the length...Ch. 8.CT - Give each formula. a The formula for the area of a...Ch. 8.CT - Determine whether the statement is true or false....Ch. 8.CT - If the area of rectangle ABCD is 46 cm2, find the...Ch. 8.CT - In square feet, find the area of EFGH. _Ch. 8.CT - Find the area of rhombus MNPQ given that QN=8 ft...Ch. 8.CT - Use Herons Formula, A=s(sa)(sb)(sc), to find the...Ch. 8.CT - In trapezoid ABCD, AB=7 ft and DC=13 ft. If the...Ch. 8.CT - A regular pentagon has an apothem of length 4.0...Ch. 8.CT - For the circle shown below, the length of the...Ch. 8.CT - Where , find the approximate length of AC. lAC_Ch. 8.CT - Where 3.14, find the approximate area of a circle...Ch. 8.CT - In the figure, a square is inscribed in a circle....Ch. 8.CT - Find the exact area of the 1350 sector shown. _Ch. 8.CT - Find the exact area of the shaded segment. _Ch. 8.CT - The area of a right triangle whose sides have...Ch. 8.CT - Pascual is remodeling a house and plans a complete...

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